I always hated in school when the teacher would instruct us to use our imaginations to solve problems. Well, hmm. Especially as a kid, my imagination was filled with magic. Not very useful. Not that you shouldn't use your imagination. You should. But as an instruction, I find it lacking. The teachers were just being lazy.
See, the thing I learned through a lot of experiments and reading is that our imagination is very powerful if you use it correctly. But much as our computers can run any possible program, our minds can imagine any situation. The key to using our imagination effectively is to learn to harness the infinite potential and direct it to a purpose.
One set of techniques I studied was called Neuro Linguistic Programming. It is thoroughly interesting, especially the earliest stuff, but avoid the cultish seminars. The early stuff was based on Cybernetics and linguistics (specifically Noam Chomsky's transformational grammar). It was quite rigorous as far as informal studies go. It has since become a new-age movement. Tread carefully if you wish to explore it.
One of the most intriguing aspects of NLP is that it teaches you to discover the structure of a mental process through introspection in terms of the raw sensory experience. That is, what do you see, hear, feel, etc. You break it down into the smallest steps that can be measured. You can then understand your own process and give yourself more control over your own apparatus. It sounds like a structured use of imagination. By deconstructing your imagination and guiding another person through the steps, you can transfer the outline of a skill to someone else.
I know this must sound like magic. But don't we expect teachers to pass skills on to others? Teachers routinely break down skills to teach them in a process known as task analysis. You are simply doing it to your imagination. It's not magic. It's not instant knowledge transfer. Practice and experience still count for a lot. But it can get you pretty far.
If it still sounds like magic, all I'm saying is that you switch from A to B:
A: Pure functions are functions that don't have any side-effects. Use your imagination.
B: To determine if a function is a pure function, look through the function line-by-line. On each line, imagine a green checkmark if the line has no side-effects. Imagine a red X if it has side-effects. When all lines have been marked, if you have any red X's, your function is not pure.
While correct, the first explanation gives very little help to your imagination. In fact, my first response to explanations of type A is to think about what it might mean. But I can use my imagination with effort. When I do that, I realize that I am imagining visually scanning the function (in my mind's eye) and marking lines with side-effects.1 The second one asks you to imagine just that. Asking someone to go through a process makes it clearer.2
NLP does have a lot of merit, especially when it comes to teaching. Our mental processes can be introspected, analyzed, and described. And we can then guide a student through a process similar to what goes on in our heads when we solve the problem. This is the last piece I need to tell the story of one of the most successful things I have ever taught. Next time.
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This is a slight lie. I don't use visual checkmarks. I actually feel different when I see an expression with a side-effect. The feeling infects the whole function it is in once I feel it. My feelings have modeled the scoping rules of the language. This is the ultimate goal of imagination and skill development--when your simulation is accurate enough to be relied on.↩
There is another improvement which I'll get to in the very next post. It will pull together the last few teaching posts.↩